Related papers: Randomized Wavelets on Arbitrary Domains and Appli…
This is the first paper in a sequence of studies in which we introduce a new type of neural networks (NNs) -- wavelet-based neural networks (WBNNs) -- and study their properties and potential for applications. We begin this study with a…
The random vector functional link (RVFL) network is well-regarded for its strong generalization capabilities in the field of machine learning. However, its inherent dependencies on the square loss function make it susceptible to noise and…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
We present here a simple construction of a wavelet system for the three-dimensional ball, which we label \emph{Radial 3D Needlets}. The construction envisages a data collection environment where an observer located at the centre of the ball…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
We consider some reduction from nonlinear Vlasov-Maxwell equation to rms/rate equations for second moments related quantities. Our analysis is based on variational wavelet approach to rational (in dynamical variables) approximation. It…
Statistical analysis of magnetic resonance imaging (MRI) can help radiologists to detect pathologies that are otherwise likely to be missed. Deep learning (DL) has shown promise in modeling complex spatial data for brain anomaly detection.…
(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems in applications are defined on bounded intervals or domains. Therefore, it is important in both…
This paper examines the possibility of, and the possible advantages to learning the filters of convolutional neural networks (CNNs) for image analysis in the wavelet domain. We are stimulated by both Mallat's scattering transform and the…
Anomaly detection in MRI is of high clinical value in imaging and diagnosis. Unsupervised methods for anomaly detection provide interesting formulations based on reconstruction or latent embedding, offering a way to observe properties…
Mathematical formulations and proofs for a wavelet based statistic employed in functional data analysis is elaborately discussed in this report. The propositions and derivations discussed here apply to a wavelet based statistic with hard…
Resting-state functional MRI (rs-fMRI) in functional neuroimaging techniques have improved in brain disorders, dysfunction studies via mapping the topology of the brain connections, i.e. connectopic mapping. Since, there are the slight…
Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
Wavelet-based segmentation approaches are widely used for texture segmentation purposes because of their ability to characterize different textures. In this paper, we assess the influence of the chosen wavelet and propose to use the…
Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the…
The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last…
We study the possibility of completing data bases of a sample of governance, diversification and value creation variables by providing a well adapted method to reconstruct the missing parts in order to obtain a complete sample to be applied…